00:01
This question has three parts to it.
00:01
It's asking us to solve for t.
00:04
So for part a, i have e to the negative 0 .01t is equal to 1 ,000.
00:10
Well, we learned from our book that we can get this out of the exponent by using our natural logs.
00:19
So to start off this problem, i'm just going to put natural log on both sides.
00:26
And in doing so, for this one, i can use my power rule to put this exponent out in the front.
00:36
So i get negative 0 .01t times natural log of e is equal to the natural log of 1000.
00:47
And then natural log of e is just 1.
00:50
So i get negative 0 .01 t is equal to the natural log of 1 ,000.
00:57
And then just dividing both sides by negative 0 .01 i get that t is equal to negative 100 natural log of 1 ,000 and that's because 1 divided by 0 .01 is 100 so that's my answer for part a for part b we're given that e to the k t is equal to 1 over 10 so again my first step is i'm going to put a natural log on both sides and as we saw before basically these just kind of cancel out because my power rule and i just end up with the exponent so here natural log of be those just kind of cancel out some left with k t is equal to the natural log of 1 over 10 however we know from our reciprocal rule that this is actually just a negative natural log of 10 and then just divide by k on both sides and i get that t is equal to the negative natural log of 10 divided by k...